Non-isothermal transport of multi-phase fluids in porous media. Constitutive equations

TL;DR

This paper develops comprehensive constitutive equations for multi-phase, multi-component flow in porous media considering thermal, compositional, and pressure gradients, including new effects like non-Darcy flow and thermal osmosis.

Contribution

It introduces novel constitutive equations that incorporate effects of varying porosity and surface tension, advancing understanding of non-isothermal multi-phase flow in porous media.

Findings

New constitutive equations for multi-phase flow under thermal and compositional gradients.

Explanation of non-Darcy behavior due to porosity and surface tension variations.

Proposal of experimental tests for Onsager symmetry in transport coefficients.

Abstract

We develop constitutive equations for multi-component, multi-phase, macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of the volume and surface averaged pressure and the saturation, and the respective driving forces from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of a thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.